LCM of 4 and 15

LCM of 4 and 15 is the smallest number among all common multiples of 4 and 15. The first few multiples of 4 and 15 are (4, 8, 12, 16, 20, 24, . . . ) and (15, 30, 45, 60, 75, 90, 105, . . . ) respectively. There are 3 commonly used methods to find LCM of 4 and 15 - by prime factorization, by division method, and by listing multiples.

Answer: LCM of 4 and 15 is 60.

Explanation:

The LCM of two non-zero integers, x(4) and y(15), is the smallest positive integer m(60) that is divisible by both x(4) and y(15) without any remainder.

Let's look at the different methods for finding the LCM of 4 and 15.

• By Division Method
• By Listing Multiples
• By Prime Factorization Method

LCM of 4 and 15 by Division Method

To calculate the LCM of 4 and 15 by the division method, we will divide the numbers(4, 15) by their prime factors (preferably common). The product of these divisors gives the LCM of 4 and 15.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 4 and 15. Write this prime number(2) on the left of the given numbers(4 and 15), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (4, 15) is a multiple of 2, divide it by 2 and write the quotient below it. Bring down any number that is not divisible by the prime number.
• Step 3: Continue the steps until only 1s are left in the last row.

The LCM of 4 and 15 is the product of all prime numbers on the left, i.e. LCM(4, 15) by division method = 2 × 2 × 3 × 5 = 60.

LCM of 4 and 15 by Listing Multiples

To calculate the LCM of 4 and 15 by listing out the common multiples, we can follow the given below steps:

• Step 1: List a few multiples of 4 (4, 8, 12, 16, 20, 24, . . . ) and 15 (15, 30, 45, 60, 75, 90, 105, . . . . )
• Step 2: The common multiples from the multiples of 4 and 15 are 60, 120, . . .
• Step 3: The smallest common multiple of 4 and 15 is 60.

∴ The least common multiple of 4 and 15 = 60.

LCM of 4 and 15 by Prime Factorization

Prime factorization of 4 and 15 is (2 × 2) = 2² and (3 × 5) = 3¹ × 5¹ respectively. LCM of 4 and 15 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2² × 3¹ × 5¹ = 60.
Hence, the LCM of 4 and 15 by prime factorization is 60.

☛ Also Check:

• LCM of 11 and 18 - 198
• LCM of 16, 20 and 24 - 240
• LCM of 20, 30 and 40 - 120
• LCM of 45 and 60 - 180
• LCM of 4, 7 and 10 - 140
• LCM of 12, 15, 20 and 54 - 540
• LCM of 12 and 25 - 300

FAQs on LCM of 4 and 15

What is the LCM of 4 and 15?

The LCM of 4 and 15 is 60. To find the LCM of 4 and 15, we need to find the multiples of 4 and 15 (multiples of 4 = 4, 8, 12, 16 . . . . 60; multiples of 15 = 15, 30, 45, 60) and choose the smallest multiple that is exactly divisible by 4 and 15, i.e., 60.

What is the Least Perfect Square Divisible by 4 and 15?

The least number divisible by 4 and 15 = LCM(4, 15)
LCM of 4 and 15 = 2 × 2 × 3 × 5 [Incomplete pair(s): 3, 5]
⇒ Least perfect square divisible by each 4 and 15 = LCM(4, 15) × 3 × 5 = 900 [Square root of 900 = √900 = ±30]
Therefore, 900 is the required number.

How to Find the LCM of 4 and 15 by Prime Factorization?

To find the LCM of 4 and 15 using prime factorization, we will find the prime factors, (4 = 2 × 2) and (15 = 3 × 5). LCM of 4 and 15 is the product of prime factors raised to their respective highest exponent among the numbers 4 and 15.
⇒ LCM of 4, 15 = 2² × 3¹ × 5¹ = 60.

If the LCM of 15 and 4 is 60, Find its GCF.

LCM(15, 4) × GCF(15, 4) = 15 × 4
Since the LCM of 15 and 4 = 60
⇒ 60 × GCF(15, 4) = 60
Therefore, the GCF (greatest common factor) = 60/60 = 1.

What is the Relation Between GCF and LCM of 4, 15?

The following equation can be used to express the relation between GCF and LCM of 4 and 15, i.e. GCF × LCM = 4 × 15.